The effect of cyclone-anticyclone asymmetry at small Rossby numbers

Abstract

Cyclone-anticyclone asymmetry in a rotating fluid results in vortices with cyclonic rotation being attenuated more rapidly than vortices with anticyclonic rotation due to the Ekman bottom friction. To explain this effect, some authors invoked rather complex integral (averaged along the vertical) models with the parametrization of nonlinear friction. A simple analytical model, free of the procedure of formal averaging and based on a separate consideration of the equations for external flow in the nonviscous region and internal flow in the boundary layer, is investigated in this work. The corresponding equations are written in the so-called geostrophic momentum approximation, which makes it possible to take into account the nonlinear advective mass transport in the boundary layer at small Rossby numbers. The nonlinear equation of the hyperbolic type for the tangential velocity, which describes the process of attenuation of an axisymmetric vortex, is obtained from the condition of total mass conservation. Based on the solutions to this equation, it was shown that distinctions in the character of vortex attenuation are caused by deviations from the geostrophic regime in the nonviscous region. It was established that the concentration (compression) of anticyclonic vortices and the extension of cyclonic ones take place in the process of attenuation.